A286317 Number of species of partial Latin squares of size n.

1, 2, 5, 18, 59, 306, 1861, 15097, 146893, 1693416, 22239872, 327670703

Offset

1,2

Comments

The size of a partial Latin square (PLS) is the number of filled entries, not the order of the matrix. The species of a PLS are all those PLSs you can get by permuting the rows, columns and symbols, and also by permuting these three roles themselves. Empty rows and columns are ignored.

Links

Table of n, a(n) for n=1..12.

H. Dietrich and I. M. Wanless, Small partial Latin squares that embed in an infinite group but not into any finite group, J. Symbolic Comput., Volume 86, May-June 2018, Pages 142-152. DOI 10.1016/j.jsc.2017.04.002.

Raúl M. Falcón, Rebecca J. Stones, Enumerating partial Latin rectangles, arXiv:1908.10610 [math.CO], 2019.

Crossrefs

Cf. A003090 (analog of this sequence, but for completed Latin squares), A286318 (for the same objects as this sequence, but with the extra requirement of being connected).

Sequence in context: A148423 A148424 A148425 * A303174 A148426 A321099

Adjacent sequences: A286314 A286315 A286316 * A286318 A286319 A286320

Keyword

nonn,more

Author

Ian Wanless, May 06 2017

Status

approved